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Parametric Survival Analysis: Weibull and Exponential Methods01:14

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A new two-parameter Rayleigh distribution: Statistical properties, actuarial measures, regression analysis, and

Ahmed M Gemeay1, Eslam Hussam2,3, Ehab M Almetwally4,5

  • 1Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt.

Heliyon
|December 16, 2024
PubMed
Summary

A new two-parameter distribution, derived from the Rayleigh distribution, offers improved lifetime modeling. This novel statistical tool demonstrates superior fit and practical utility in actuarial science and insurance data analysis.

Keywords:
EstimationGeneralized distributionInsuranceReal dataRegressionSimulation

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Area of Science:

  • Statistics
  • Probability Theory
  • Actuarial Science

Background:

  • The Rayleigh distribution is a foundational model in various scientific fields.
  • Accurate lifetime data modeling is crucial in actuarial science and insurance.
  • Existing distributions may not fully capture the complexities of certain lifetime datasets.

Purpose of the Study:

  • Introduce a novel two-parameter distribution extending the Rayleigh distribution.
  • Investigate the mathematical properties and estimation techniques for the new distribution.
  • Evaluate the practical applicability and performance of the proposed distribution in real-world scenarios.

Main Methods:

  • Derivation of a new two-parameter distribution from the Rayleigh distribution.
  • Application of parameter estimation techniques.
  • Conducting extensive simulation studies to analyze asymptotic behavior of estimators.
  • Calculation of actuarial measures and regression analysis.
  • Modeling a real-world lifetime dataset from the insurance industry.

Main Results:

  • The proposed distribution exhibits robust mathematical properties.
  • Simulation studies confirm the asymptotic behavior of the model estimators.
  • Actuarial measures and regression analysis validate the distribution's practical utility.
  • The new distribution demonstrates a superior fit to insurance lifetime data compared to existing models.

Conclusions:

  • The novel two-parameter distribution is a valuable addition to statistical modeling tools.
  • It offers enhanced capabilities for accurate lifetime data analysis, particularly in actuarial science.
  • The distribution shows significant promise for both theoretical research and practical applications in data-intensive fields.